von Delft Group

Correlated open quantum systems

Research in our group focusses on open correlated quantum systems. The combination of "open" and "correlated" leads to many fascinating phenomena in experiment, and poses interesting methodological challenges for theoretical work. We are particularly interested in electron transport in interacting mesoscopic and nanoscale systems, such as quantum dots, quantum wires, quantum point contacts and disordered conductors, and in the driven dynamics of local degrees of freedom coupled to a dissipative bath, such as an exciton tunnel-coupled to an electron gas.

The figure describes the absorption rate for light incident on a quantum dot coupled to a fermionic reservoir to realize Kondo exciton. The measured line-shapes (dots) depend strongly on magnetic field (different colors), in a way that implies tunable Anderson orthogonality exponents, and that is well described by numerical results obtained by the numerical renormalization group (solid lines).[From Latta et al., Nature, 474, 627 (2011).

Numerical approaches

Transport through a quantum point contact: a paradigmatic
example of an open, correlated quantum system, where interactions
lead to striking anomalies in the conductance (0.7-anomaly).
[from Bauer, Heyder et al., Nature, 501, 73 (2013).]

Since experimentally relevant models are very often too complicated to admit a full analytical treatment, much of our work has a significant numerical component. The two approaches that we currently rely on most are the functional renormalization group (fRG), and numerical tensor network methods methods for treating quantum impurity models.

fRG is in essence an RG-enhanced way of doing perturbation theory in the interaction. We have recently developed a version of this approach suitable for studying (not-too-strongly) interacting open quantum

systems that lack translational symmetry. We have used it to develop a microscopic understanding of the 0.7-anomaly in quantum point contacts, and are currently extending our treatment of this system to include various types of complications, such as spin-orbit interactions or superconducting correlations, and nonequilibrium transport using Keldysh-fRG.

Tensor networks and quantum impurity models

The magnetoresistivity of a disordered gold wire with a dilute
amount of iron impurities, for several temperatures. This system is
described by a spin-3/2, 3-channel Kondo model. Solid lines are
measurements, dashed-lines are no-free-parameter predictions obtained
with the numerical renormalization group, while exploiting the
non-Abelian symmetry group U(1)xSU(3). [From Hanl et al.,
Phys. Rev. B, 88, 075146 (2013).]

Our interest in tensor networks has evolved in the context of quantum impurity models, which describe discrete quantum degrees of freedom coupled to a bath of excitations. The most powerful numerical method for treating such systems has for many years been the numerical renormalization group (NRG). We realized about 10 years ago that this method has the same mathematical basis as the density matrix renormalization group (DMRG) for solving 1-dimensional quantum chain models, in that both employ matrix product states (MPS), a one-dimensional example of a tensor network.

My coworker Anreas Weichselbaum has exploited this fact to develop a uniquely flexible and optimized 1d-tensor network code that combines advantages of both methods and exploits non-Abelian symmetries, resulting in a very powerful and versatile tool for treating interacting low-dimensional quantum systems. We are currently working to implement non-Abelian symmetries also in codes for two-dimensional tensor networks.